A solution to an open problem on the T-product of TL-fuzzy subgroups

Many studies have investigated necessary and sufficient conditions whereby fuzzy subgroups of a Cartesian product of groups are a Cartesian product of fuzzy subgroups. Chon [Fuzzy subgroups as products, Fuzzy Sets and Systems 141 (2004) 505–508] found such conditions under minimum operation. He pointed out that the problem of finding necessary and sufficient conditions for T-fuzzy subgroups under a t-norm operation is still open. In this study, we solve the problem and identify necessary and sufficient conditions under t-norm operation.